10368 has 40 divisors (see below), whose sum is σ = 30855. Its totient is φ = 3456.

The previous prime is 10357. The next prime is 10369. The reversal of 10368 is 86301.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as 4! ⋅ (3!)^{3} ⋅ 2!.

10368 is nontrivially palindromic in base 15.

10368 is an esthetic number in base 11, because in such base its adjacent digits differ by 1.

It can be written as a sum of positive squares in only one way, i.e., 5184 + 5184 = 72^2 + 72^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=72.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 12.

It is a self number, because there is not a number *n* which added to its sum of digits gives 10368.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 10368.

It is not an unprimeable number, because it can be changed into a prime (10369) by changing a digit.

10368 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 3455 + 3456 + 3457.

10368 is a Friedman number, since it can be written as 6^(3+1)*(8+0), using all its digits and the basic arithmetic operations.

2^{10368} is an apocalyptic number.

10368 is a gapful number since it is divisible by the number (18) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 10368

10368 is an abundant number, since it is smaller than the sum of its proper divisors (20487).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

10368 is an frugal number, since it uses more digits than its factorization.

10368 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 26 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 18.

The square root of 10368 is about 101.8233764909. The cubic root of 10368 is about 21.8054471140.

Multiplying 10368 by its sum of digits (18), we get a square (186624 = 432^{2}).

10368 divided by its sum of digits (18) gives a square (576 = 24^{2}).

Adding to 10368 its reverse (86301), we get a palindrome (96669).

It can be divided in two parts, 103 and 68, that added together give a palindrome (171).

The spelling of 10368 in words is "ten thousand, three hundred sixty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 288 324 384 432 576 648 864 1152 1296 1728 2592 3456 5184 10368

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